Measures of centrality for multivariate and directional distributions

DOI10.2307/3314859zbMath0622.62054OpenAlexW2062129224MaRDI QIDQ3759726

Christopher G. Small

Publication date: 1987

Published in: Canadian Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/3314859

zbMATH Keywords

affine transformationsequivariancedirectional distributionsmonotone transformationsmeasures of centralityfinite-dimensional Euclidean spaceHotelling- Chamberlin pointmultivariate version of median

Mathematics Subject Classification ID

Multivariate analysis (62H99) Geometric probability and stochastic geometry (60D05) Characterization and structure theory for multivariate probability distributions; copulas (62H05) Foundations and philosophical topics in statistics (62A01)

Related Items (21)

The influence function and maximum bias of Tukey's median ⋮ On The ConditionalL₁-median and its estimation ⋮ Halfspace depth for general measures: the ray basis theorem and its consequences ⋮ Robustness of the half-space median ⋮ On the computation of multivariate scenario sets for the skew-\(t\) and generalized hyperbolic families ⋮ Recent advances in directional statistics ⋮ On directional multiple-output quantile regression ⋮ Equivariance-based analysis of PDE evolutions related to multivariate medians ⋮ Distance-based directional depth classifiers: a robustness study ⋮ Half-space depth of log-concave probability measures ⋮ Another look at halfspace depth: flag halfspaces with applications ⋮ Centrality as a gradual notion: a new bridge between fuzzy sets and statistics ⋮ A nonparametric multivariate multisample test based on data depth ⋮ Tukey’s Depth for Object Data ⋮ On min-max majority and deepest points ⋮ Characterizing angular symmetry and regression symmetry. ⋮ Halfspace depth and floating body ⋮ Influence functions for a general class of depth-based generalized quantile functions ⋮ Jensen's inequality for multivariate medians ⋮ On the optimality of the max-depth and max-rank classifiers for spherical data. ⋮ General notions of statistical depth function.

Uses Software

• AS 78

Cites Work

• Unnamed Item
• Limit theorems for empirical processes
• Optimal Strategies for Second Guessers
• A simple test for uniformity of a circular distribution

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